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Adventures in Thermochemistry

James S. Chickos*

Department of Chemistry and Biochemistry

University of Missouri-St. Louis

Louis MO 63121

E-mail: [email protected]

5

Union Station STL

Previously we concluded the following:

- 1. Vaporization enthalpies at the boiling temperature are predicted to approach a limiting value
- 2. Boiling temperatures appear to converge to a finite limit.
- Critical temperature and boiling temperatures appear to converge as a function of the number of repeat units.
- 4. Critical pressures appear to converge to 1 atm as the number of repeat units .
- 5. Enthalpies of transfer appear to show curvature with increasing size

Can any more of this be experimentally verified?

Applications of Correlation Gas Chromatography

Vapor Pressure

Requirements: Vapor pressures of the standards preferably as a function of temperature over a range of temperatures

Applications of Correlation Gas Chromatography

Vapor Pressure

Using the following series of hydrocarbons as examples:

Retention Times as a Function of Temperature

ta = ti –tCH4

Solvent: CH2Cl2

Plots of ln(to/ta) vs 1/T

A plot of natural logarithm of the reciprocal adjusted retention times ln(to/ta) for (top to bottom): ,n- octane; , 1-nonene; , n-decane; , naphthalene;

, n-dodecane; , n-tridecane as a function of 1/T; to = 1 min.

Equations resulting from a linear regression

of ln(to/ta) versus (1/T)K-1

Compound ln(to/ta)=- slngHm/RT + ln(Ai)

n-octane ln(to/ta)= (-32336/RT) + (11.064) r2=0.9995

1-nonene ln(to/ta)= (-35108/RT) + (11.159) r2=0.9993

n-decane ln(to/ta)= (-38973/RT) + (11.655) r2=0.9994

naphthalene ln(to/ta)= (-41281/RT) + (11.176) r2=0.9997

n-dodecane ln(to/ta)= (-46274/RT) + (12.685) r2=0.9996

n-tridecane ln(to/ta)= (-50036/RT) + (13.232) r2=0.9997

to = 1 min

A Plot of ln(p/po)exp vs ln(to/ta)

octane

decane

dodecane

tridecane

A plot of experimental vapor pressures ln(p/po) against ln(to/ta) at T = 298.15 K; to = 1 min; po= 101 kPa

Results of Correlating ln(to/ta) with ln(p/po) at T = 298.15 K

slngHm(368 K) ln (A) ln(to/ta) ln(p/po) ln(p/po) ln(p/po)

lita calc lit

octane -32336 11.064 -1.98 -3.99 -3.95

1-nonene -35108 11.159 -3.00 -5.15 -4.96b

decane -38973 11.655 -4.07 -6.32 -6.39

naphthalene -41281 11.176 -5.48 -8.04 -7.98c

dodecane -46274 12.685 -5.98 -8.63 -8.63

tridecane -50036 13.232 -6.95 -9.79 -9.76

ln(p/po) = (1.1820.015) ln(to/ta) -(1.53 0.059); r2 = 0.9987

Vapor pressures for naphthalene are for the liquid

aRuzicka, K.; Majer, V. J. Phys. Chem. Ref. Data 1994, 23, 1-39;

bPhysical Properties of Chemical Compounds II, Dreisbach, R. R. Advances in Chemistry Series 22, ACS, Washington: DC.

cChirico, R. D.; Knipmeyer, S. E.; Nguyen, A. Steele, W. V. J. Chem. Thermodyn. 1993, 25, 1461-4.

Provided vapor pressures of the standards are available as a function of temperature, this correlation can be repeated at other temperatures so that a vapor pressure temperature profile can be obtained.

Applying this protocol as a function of temperature at T = 15 K intervals and fitting the data for 1-nonene and naphthalene to a third order polynomial results in:

a predicted boiling temperature for nonene of : 421 K (420 K lit)

a predicted boiling temperature for naphthalene of: 507 K (493 K lit)

Vapor Pressures by Gas Chromatography

Vapor pressure of an analyte off a column is inversely proportion to it adjusted retention, 1/ta.

Why is 1/ta proportional to the vapor pressure of the pure material when the enthalpy of transfer is a measure of both the vaporization enthalpy and the interaction on the column?

slngHm(Tm) = lgHm(Tm) + slnHm(Tm)

Daltons Law of Partial Pressures pT = panalyte + pstationary phase = panalyte

Raoult’s Law:: the vapor pressure of component a is equal to the product of vapor pressure of pure a (pao) times its mole fraction, χa

pa(obs) = pao·χa

Since the stationary phase is a polymer, χa≈ 1

The effects of slnHm(Tm) are small and compensated by the standards.

Returning to the n-alkanes

Vapor Pressures of the Standards

- literature vapor pressure evaluated using the Cox equationa
- ln (p/po) = (1-Tb/T)exp(Ao +A1T +A2T 2)

po = 101.325 kPa

- aRuzicka, K.; Majer, V. Simultaneous Treatment of Vapor Pressures and Related Thermal data Between the Triple Point and Normal Boiling Temperatures for n-Alkanes C5-C20. J. Phys. Chem. Ref. Data 1994, 23, 1-39.

Equations for the temperature dependence of ln(to/ta) for C14 to C20 where to = 1 min:

ln(to/ta) = -slnHm(Tm)/R*1/T + intercept

ln(p/po) = (1.27 0.01) ln(to/ta) - (1.693 0.048); r 2 = 0.9997

Vapor pressures of n-alkanes (C14 to C20) at T = 298.15 K:

unknown

-13.3

-13.3

?

po = 101.325 kPa

Correlation between ln(1/ta) calculated by extrapolation to T = 298.15 K versus ln(p/po) calculated from the Cox equation for C14 to C20 (po = 101.325 kPa)

ln(p/po) = (1.27 0.01) ln(to/ta) - (1.693 0.048); r 2 = 0.9997

Correlations of Vapor Pressures of Hexadecane from T/K = (298.15 to 500) K

500 K

Vapor pressure -temperature dependence for hexadecane;

line: vapor pressure calculated from the Cox equations for C14,

circles; vapor pressures calculated by correlation treating hexadecane as an

unknown and correlating ln(to/ta) with ln(p/po) for C14, C15, C17-C20 as a function

of temperature from T = (298.15 to 500) K.

Normal boiling temperature: 560.2 (expt); 559.9 (calcd)

By a process of extrapolation, vapor pressures of C17 to C20 were used to evaluate C21 to C23; C19 to C23 were used to evaluate C24 and C25, ...

By such a process of extrapolation, vapor pressure equations were obtained for C21 through to C38 using commercially available samples from T = (298.15 to 540) K at 30 K intervals and the resulting vapor pressures were fit to the following third order equation which has been found to extrapolate well with temperature:

ln(p/po) = A (T/K)-3 + B(T/K)-2 + C(T/K)-1 + D;

Using this equation the boiling temperatures of C21 to C38 could be predicted

Some Available Comparisons With Direct Measurements

aLiterature value. b This work. c Mazee, W. M., “Some properties of hydrocarbons having more than twenty carbon atoms,” Recueil trav. chim 1948, 67, 197-213. Francis, F.; Wood, N. E., The boiling points of some higher aliphatic n-hydrocarbons, J. Chem. Soc. 1926, 129, 1420.

Experimental vapor pressures for the n-alkanes larger than C38 are not available. What are available are estimated values.a,b The values are available in the form of a program called PERT2 that runs in Windows

Using vapor pressures calculated from C24 through to C38, values for C40 through to C76 were evaluated.

PERT2 is a FORTRAN program written by D. L. Morgan in 1996 which includes parameters for n-alkanes from C1 to C100 and heat of vaporization and vapor pressure correlations. The parameters for C51 to C100 are unpublished based on the critical property (Tc, Pc) correlations of Twu and the Kudchadker & Zwolinski extrapolation of n-alkane NBPs presented in Zwolinski & Wilhoit (1971).

a Morgan, D. L.; Kobayashi, R. Extension of Pitzer CSP models for vapor pressures and heats of vaporization to long chain hydrocarbons.Fluid Phase Equilib. 1994, 94, 51–87.

b Kudchadker, A. P.; Zwolinski, B. J. Vapor Pressures and Boiling Points of Normal Alkanes, C21 to C100. J. Chem. Eng. Data 1966, 11, 253.

a Kudchadker, A. P.; Zwolinski, B. J. Vapor Pressures and Boiling Points of Normal Alkanes, C21 to C100. J. Chem. Eng. Data 1966, 11, 253.

The vapor pressures were fit to the following third order polynomial:

ln(p/po) = A(T/K)-3 + B(T/K)-2 +C(T/K) + D

Using the constants of the previous slide, the normal boiling temperatures were predicted by extrapolation.

A plot of the normal boiling temperatures of the n-alkanes as a function of the number of methylene groups resulted in the following:

N = the number of carbon atoms. The solid symbols represent the experimental and the others the calculated boiling temperatures of C3 to C92. The dotted line was calculated for the n-alkanes using a limiting boiling temperature of TB(∞) = 1076 K. The solid line was obtained by using a by fitting the experimental data to the hyperbolic function previously described and a value of TB(∞) = (1217 ± 246) K

Conclusions:

Based on the data available, it appears that boiling temperature appear consistent with the prediction that boiling temperatures would approach a limiting value. The agreement with average value of 1217 obtained previously is probably fortuitous

Rachael Maxwell, Boy friend, Richard Heinze Dmitry Lipkind Darrel Hasty

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